A. Technical Field
The present invention relates generally to compensation of amplitude and quadrature phase errors (including those generated by polyphase filters) generated within the analog, front-end of an RF receiver, and more particularly, to the correction of these errors in the digital and frequency domains within the receiver.
B. Background of the Invention
When designing highly integrated monolithic receivers, a significant challenge is the provision of channel selectivity. For direct conversion or zero-IF receivers, the channel selectivity is provided by symmetrical low-pass filtering after the quadrature down-conversion mixers. This filtering may comprise a combination of analog and digital filters such that the overall transfer function meets the desired selectivity requirements. It is important that strong interfering signals are sufficiently attenuated by the analog selectivity such that they do not exceed the linear range of analog-to-digital converters or of any of the analog stages in the baseband signal path.
Such direct conversion receivers present additional challenges in the form of:                (1) DC offsets that are by definition in the center of the desired passband        (2) 1/f noise, which can have high spectral density at the center of the passband; and        (3) 2nd order inter-modulation in the down-conversion mixers, which can cause interferers to mix with themselves to produce time-varying signals at baseband corresponding to the AM modulation envelope of the interferers in question.        
Mitigation of these typical direct conversion problems forms a large part of the design effort when using direct conversion architectures; but in the case of narrow-band signaling formats, it is by no means certain that these parasitic in-band signals can be adequately suppressed. In such cases, it is common to consider low-IF (hereinafter, “LIF”) or near-zero IF (hereinafter, “NZIF”) receivers.
A low-IF receiver is often configured such that the image channel is also the left or right adjacent channel of the wanted signal, (i.e., the center frequency of the baseband signal is equal to half the channel spacing). In such a case, DC offset is just barely out-of-band as illustrated in FIG. 1.
A major advantage of the NZIF approach is that the unwanted issues described above, including the centered DC offset, are out-of-band. However, a challenge of the NZIF approach is that of obtaining sufficient image rejection selectivity. The use of low-pass filter centered around the DC offset will have an equal impact on both the wanted and unwanted image responses. Unless the ADCs have sufficient dynamic range to simultaneously handle the largest possible unwanted signal at the image frequency and a threshold sensitivity signal at the wanted signal, asymmetric analog filtering may be required. Such asymmetric filtering can be realized with a class of filters known as a poly-phase filter (PPF). The context and system architecture 210 for using polyphase filters 220 in a receiver as described above is illustrated in FIG. 2.
The term poly-phase filter means a filter that is created by the shift transform from its low-pass prototype, (i.e., s→(s−jωα)) so that the frequency is no longer centered around the DC offset, but can be arranged such that passband is centered around the wanted signal at some positive frequency while rejecting an image response at a corresponding negative frequency. In a typical analog implementation, the frequency shifting transform cannot be realized with real components. However, in a quadrature down-conversion receiver architecture with differential signals for I and Q, all four quadrature phases of the received signal are available, making it possible to implement polyphase filter topologies.
In order to calculate a frequency response, a phase relationship is defined between the 2 input ports 310, 320 (or 4 input terminals) of the network as shown in FIG. 3. For illustrative purposes only, assume that for a positive frequency the relative phase of inputs to R1 330, R2 331, R3 332, and R4 333 are 0, 90, 180 and 270 degrees respectively. FIG. 4 illustrates a calculated frequency response 410 of the network in FIG. 3 assuming all of the resistors are 50 ohms and all of the capacitors are 5 picofarads.
One skilled in the art will recognize that a major problem with this kind of polyphase filter is the reliance on cancelation to obtain a desired stop-band rejection. The degree of cancellation is effectively dependent on statistical component matching, which is a problem that cannot be entirely eliminated with analog filter elements.
The problems caused by mismatch become more apparent when considering a higher order bandpass filter. As an example, consider a 4-pole Butterworth active polyphase filter, based on two cascaded Tow-Thomas biquad sections. FIG. 5 illustrate an exemplary single section 510 of the filter (i.e., the bi-quad filter would have another section in series to the one illustrated in FIG. 5). For purposes of illustration, fully differential op-amps are represented by ideal voltage-controlled voltage sources 520 each with a voltage gain of −105.
For purposes of comparison, FIG. 6 illustrates a response 610 in which nominal component deviation is used. In order to investigate the impact of component tolerances, each R and each C is assigned a 2% standard deviation. FIG. 7 illustrates a Monte Carlo simulation of the filter response 710 in which 1,100 trials were performed with the 2% standard deviation being randomly generated across the components within the filter. FIG. 8 illustrates a further Monte Carlo simulation of the filter 810 in which 100 trials were performed within the same 2% standard deviation being randomly generated across the components. One skilled in the art will recognize the unwanted image responses 720, 820 located on the left side of the passband.
As can be observed from the unwanted image responses 720 and 820, the image rejection of the polyphase filter can be significantly degraded when statistical variation of component tolerances is considered, so that the amount of image rejection that can be relied upon is significantly reduced.
Worse still, it should be noted that the above analysis only measures one frequency at a time during the frequency sweep. Under conditions of component mismatch, not only is the amount of attenuation at the negative frequencies reduced, but there is a propensity to also create a positive frequency component at the same time, due to the fact that filter responses at output ports 1 and 2 are no longer identical. This is because for any given Monte Carlo trial, the filter responses (especially in the rejection band) can be very different and can be more graphically illustrated by viewing the corresponding plots for a single trial shown in FIGS. 9A and 9B.
At some frequencies, there is a very significant mismatch, and at other frequencies there is a closer match. The matching in the passband tends to be much better than the matching in the intended stop-band, where the amplitude response is highly dependent on the degree of cancellation that is achieved between nominally identical components.
Essentially, the problem that arises is one of frequency-dependent I/Q mismatch, both amplitude mismatch and quadrature phase error. Notably in the stop-band, the amplitudes of the I and Q components are no longer identical after filtering and the relative phase offset between them is no longer 90 degrees. This effectively prevents further filtering from improving the stop-band rejection unless some corrective measures are considered.
The idea of using FFT techniques to measure and compensate for frequency-dependent mismatch is known in the art, particularly in the context of OFDM communications systems, where frequency domain processing particularly convenient utilizing the existing IFFT and FFT processors that are inherently needed in the signal path. What is now needed is a system and method to assess and apply complex, frequency-dependent correction to an arbitrary time-domain signal and preferably to apply the run-time correction entirely in the time-domain, especially for signals that do not inherently require frequency domain processing. This technique will be particularly valuable for overcoming the mismatch errors introduced by analog polyphase filters, but can be generally applied to frequency-dependent quadrature and amplitude errors from a variety of sources.